A framework to quantify the inter-annual variation in near-surface air temperature due to change in precipitation in snow-free regions

A negative correlation between near-surface air temperature (Ta) and precipitation (P) has long been recognized over many land regions, but a predictive quantitative relationship has not yet been established. In this study, we examine inter-annual variations in Ta with P and investigate how the Ta-P relationship varies with aridity in regions without snow coverage. The wetness index is used as a measure of aridity (defined as the ratio of mean annual P to Eo, with Eo the net radiation expressed as an equivalent depth of water), with wetness index more (less) than 1.0 used to define the wet (dry) regions. Results show that variations in Ta are independent of P in wet environments, while in dry environments the variations in Ta with P increase with aridity. We use that relationship to establish a quantitative framework to a priori predict the Ta-P relation based on aridity. The results highlight the importance of inter-annual variations in P in changing Ta in dry environments, since it has similar magnitude with the decadal global warming signals over land.


Introduction
The near-surface air temperature (T a ) is usually higher during a low precipitation (P) year (Namias 1960, Madden andWilliams 1978). This negative T a -P relation has been very widely observed and documented at daily, intra-/inter-annual and even longer time scales over land (Trenberth and Shea 2005, Adler et al 2008, Berg et al 2015, Sharma and Mujumdar 2019. The correlation of T a and P has important implications for the concurrence of dry and hot extremes (Mueller andSeneviratne 2012, Hao et al 2013), which are expected to change in a warmer climate (Wu et al 2020). While the T a -P relation has been extensively documented in both observations and model simulations, there is, as yet, no formal quantitative theory to a priori predict the variations in T a due to those in P.
One approach to explore the impact of variations in P on T a is to investigate the relation between soil moisture and evapotranspiration (Seneviratne et al 2006, Koster et al 2009, Lorenz et al 2016, which originates from the classical soil moisture (SM) and evaporative fraction (EF) relation (Budyko 1974, Eagleson 1978. Here the underlying mechanism is for low SM to lead to a lower evaporative flux and hence an enhanced sensible heat flux (i.e. lower EF) that in turn increases T a (Seneviratne et al 2010). That form of the SM-EF relation has been widely used with fully coupled climate model simulations by separately considering both the EF-T a and SM-T a coupling (e.g. Schwingshackl et al 2017). The SM-T a interactions have been helpful to explain the T a -P relation (Vogel et al 2018), with the change of T a greatly reduced in the absence of soil moisture change in climate model simulations or vice versa (Berg et al 2015(Berg et al , 2016. One potential challenge to this approach is that the SM-EF relation may not be unique and could therefore vary with surface and meteorological conditions (Haghighi et al 2018).
The SM-EF approach has been widely recognised as a suitable conceptual framework for understanding the negative T a -P correlation. However, it is difficult to apply in many practical applications because of a lack of suitable observed SM data. In that context we seek a practical approach explicitly recognises the SM-T a coupling and SM-EF framework but can also be used with the available observations. Previous studies have shown that the correlation between T a and P is strongly negative in arid regions (e.g. figure 1 in Berg et al 2015). In addition to that correlation, Yin et al (2014) also noted that the magnitude of the variations in T a with P seems to generally increase with the background aridity. The above results led us to hypothesize that the background aridity may play a crucial role in setting the increase in T a during low P years. Furthermore, we hypothesize that it might be possible to quantitatively estimate the magnitude of T a -P relation based on the background aridity.
The aim of this paper is to quantitatively investigate the T a -P relation. We use annual data but note that the approach is, in principle, suitable for use at shorter time steps, such as monthly or seasonal time steps. We begin by briefly (re-)investigating the T a -P correlation using readily available gridded climate observations. We then go beyond previous qualitative correlations by establishing a quantitative framework to predict variations in T a due to those in P (i.e. the slope of T a -P regression) using the regional background aridity as the predictive variable. The proposed framework is tested using independent data from Texas (USA), the Murray-Darling Basin (MDB, Australia) and a hyper-arid region in western Australia.

Climate data
Radiation and meteorological data are used to explore the empirical relation between the slope of the T a -P relation and aridity (wetness index is used here as the measure of aridity, see section 2.3). Global T a and P observations were sourced from the widely used Climatic Research Unit (CRU) TS4.01database (monthly, 0.5 • × 0.5 • , 1901-2016) (Harris et al 2014). To quantify the aridity, we use the abovenoted CRU precipitation data supplemented by radiation data from the NASA/GEWEX Surface Radiation Budget (SRB) Release-3.0 (monthly, 1 • × 1 • , 1984-2007) database (Stackhouse et al 2011). The SRB database documents the four surface radiative flux components (incoming and outgoing shortwave and longwave radiative fluxes), and we use those to calculate the net radiation and further calculate the aridity. We use the calendar year period 1984-2007 to define the study period and integrate the CRU T a and P databases to the spatial resolution of 1 • used in the SRB database.
To investigate the application of the empirical T a -P relation, we conduct regional case studies in three regions, i.e. Texas in USA, the Murray-Darling basin (MDB) in southeast Australia and a hyper-arid region in western Australia (West AU).
Long-term observations of T a and P in the three regions, i.e. Texas , MDB (1910MDB ( -2018 and West AU (1914 were independently sourced from the U.S. Climate Divisional Dataset (referred to as NOAA-NCEI) (Vose et al 2014, http://www.ncdc.noaa.gov/cag), the Australian Bureau of Meteorology (http://www.bom.gov.au/) and the Australian Water Availability Project (AWAP) (Raupach et al 2009(Raupach et al , 2012 respectively. The longterm data were used to estimate the relations between T a and P anomalies in the three case study regions, and the slopes of the regression were compared with the slopes predicted independently using the ariditybased T a and P relation (see section 3.3).

Spatial masks to define study extent
In order to minimise potential problems caused by inaccurate precipitation data, we restricted the analysis extent to those grid-cells that had at least one precipitation measurement station (e.g. Sun et al 2012). The aim was to restrict the analysis extent to those areas of the globe with more comprehensive P observations. In more detail, we use grid-cells having at least one precipitation measurement station for 90% of months over the 1984-2007 period to define regions with the highest possible P data quality (figure 1(a)).
To avoid any complication in this initial analysis we exclude irrigation areas because the increase in evapotranspiration due to irrigation is well known to decrease T a independently of P (Lobell et al 2009, Puma andCook 2010). To identify those grid-cells, we used a digital map from the Food and Agriculture Organization of the United Nations (Siebert et al 2013) to identify grid-cells having at least 10% of their area specified as being subject to irrigation (figure 1(b)) and those regions were excluded from the study extent. Finally, we also excluded regions having snow/ice cover to avoid complications arising from prominent seasonal changes in albedo. Gridcells that were snow/ice free (figure 1(c)) were identified using monthly data during the 2001-2007 period from the MODIS/Terra Snow Cover dataset (Hall and Riggs 2015). The final resulting mask was constructed from the above three components and identified 550 grid-cells ( figure 1(d)). The resulting mask (figure 1(d)) was held fixed over the entire study period. The study area is dominated by grid-cells in Australia, southeast Asia and southern parts of the US with a scattering of grid-cells from other continents. As shown in figure 1 the study area is mainly located at low and middle latitudes, therefore, we have cropped the maps after figure 1 to a latitude range between −50 S and 50 N.

Measure of aridity
As our measure of aridity, we use the wetness index defined in the Budyko approach as the ratio of mean annual P to as the net radiation R n expressed as an equivalent depth of water E o = R n /L, with L the latent heat of vaporisation) (Budyko 1974). This ratio has recently been found to best represent aridity in the coupled mass-energy balance at the surface in climate model output , Milly and Dunne 2016 and is consistent with the original Budyko framework (Budyko 1974). The dimensionless index was calculated at each grid-cell using the 1984-2007 mean annual P (from CRU) and E o (from SRB). The spatial distribution ofP/E o across the study region is shown in figure S1 (available online at https://stacks.iop.org/ERL/15/114028/mmedia). Grid-cells withP/E o > 1.0 are described here as wet (energy-limited) and regions whereP/E o ≤ 1.0 are described here as dry (water-limited) (Donohue et al 2007). The spatial pattern of aridity is generally consistent with previous studies (Mcvicar et al 2012, Greve and.

Variation in T a with P
We investigate the relationship between T a and P across the study region using the CRU observations for . For that, we first linearly detrended the T a and P time series (i.e. subtract the linear trend from original time series to derive the detrended anomalies) and fitted a regression to the anomalies (∆T a and ∆P) (figure 2). (The results of ∆T a -∆P regression without detrending (maps not shown) are more or less identical to (figure 2). As has been noted on many occasions previously (see papers in the Introduction), we also find that ∆T a is negatively correlated with ∆P over much of the study region ( figure 2(a)). The slope of the ∆T a -∆P regression is more negative in arid regions (e.g. central Australia, Southern and Northern Africa and Southwest US) and approaches zero in wet regions (e.g. Southeast Australia, central Africa, most of South America, Southeast US and Southeast Asia) (figure 2(b), figure S1). We also note that the ∆T a -∆P regression has, in general, a higher level of statistical significance (defined by p-value ≤ 0.05) in arid regions than in wetter regions (figure 2(c), figure S1).

Relating the ∆T a -∆P regression to aridity
To investigate how the T a -P relation varies with aridity, the slope of the ∆T a -∆P regression (see figure 2(b), and denoted as dT a /dP here) is plotted against the wetness indexP/E o (see figure S1) at each grid-cell ( figure 3). The result shows a characteristic structure with markedly negative ∆T a -∆P slopes (dT a /dP) under arid conditions (i.e.P/E o ≤ 1). In contrast, under wet conditions (i.e.P/E o > 1) the resulting slope is near zero and ∆T a is more or less independent of ∆P. We determined separate linear regressions on either side of this threshold ( figure 3).
The result indicates some scatter in the relation between slope of T a -P regression and aridity, particularly in dry conditions. That scatter is found to be separated by the statistical significance of the ∆T a -∆P regressions (see p-value in figure 2(c)), with the statistically significant regressions consistently showing more negative ∆T a -∆P slopes (figure 3).
Here we have used detrended climate data (figure 3) to calculate the anomalies, and the results show the same characteristic structure if the data are not detrended (Fig. S2) with negative ∆T a -∆P slopes under arid conditions but close to zero slopes in the wet environments. We also calculated the results using T a and P data from the University of Delaware (UoD) database (Lawrimore et al 2011) and the results were more or less the same (figure S3).

Application
Based on the empirically determined T a -P-aridity relation (figure 3), we can predict the change of T a due to P in regions that have limited influence of snow/ice cover and irrigation. To investigate application of this method, we conducted tests using independent data over three separate regions ( figure 4(a)).
Using detrended anomalies, the independent observations showed negative ∆T a -∆P relations with slopes of −0.0016 K mm −1 for Texas ( figure 4(b)), −0.0019 K mm −1 for the MDB (figure 4(c)) and −0.0022 K mm −1 for West AU ( figure 4(d)). (We obtained more or less identical results using anomalies that were not detrended ( figure S4).) To account for the aridity (P/E o ) in three case study regions, thē P and E o are calculated for the 1984-2007 period in each region. The value ofP/E o for each region was then used to predict the ∆T a -∆P relation (per figure 3) that was subsequently compared with the observations (figure 4(e)). The results show that the observation-based ∆T a -∆P relation in each of the three case study regions are predicted by the empirical regression for dry environments (figure 3, dT a /dP ∼ 0.0023P/E o -0.0023).

Discussion
A negative relation between precipitation (P) and air temperature (T a ) has long been noted over land regions. That is, years with lower than average precipitation also tend to be warmer, and vice versa. In previous work we found that the slope of the ∆T a -∆P regression appeared to become more negative as the Figure 3. Relation between slope of the ∆Ta-∆P regression (as per figure 2(b), and denoted as dTa/dP here) and the wetness index (P/Eo, figure S1) (n = 550 grid-cells). Colours (and legend) are for the p-value of the ∆Ta-∆P regression (as per figure  2(c)). Two separate linear regressions (dry environment:P/Eo ≤ 1, wet environment:P/Eo > 1) have been estimated, and full details of the regressions are shown in table S1. overall aridity increased (Yin et al 2014) but that earlier finding was only based on four regions. Here we have extended that result by examining the ∆T a -P regression over 550 (1 • × 1 • ) grid-cells using CRU-SRB grid-based observations (figure 2) that specifically exclude the influence of irrigation and snow/ice (figure 1). We further proposed an empirical relation between the ∆T a -P slopes and aridity (figure 3), which confirms and quantitatively extends the earlier finding. The empirical results show that the variations in T a are independent of P in wet environments, while in dry environments the variations in T a with P increase as the hydrologic environment becomes more arid.
Taken together those empirical results follow the long standing hydrologic notion that the responses of surface energy components to variations in P in wet and dry environments are different. In wet environments the surface energy balance (and hence T a ) is not particularly sensitive to variations in P but responds primarily to variations in energy supply, hence, the year-to-year variations in P would mostly result in year-to-year variations in runoff (Budyko 1974). In contrast, in dry environments the surface energy balance responds strongly to variations in P via variations in the four surface radiation components (incoming and outgoing short-and long-wave) and variations in the latent and sensible heat fluxes (e.g. Yin et al 2014) which alters T a .
The empirical results reported in the study provide a quantitative empirical framework to a priori predict the T a -P relation using a standard and widely used measure of aridity. With this method, one can estimate the magnitude of inter-annual variations in T a due to those in P (denoted as dT a /dP) by using piecewise linear functions separating regions for dry and wet environments (figure 3). This new framework was evaluated by independent tests in three arid regions and found to be both practical to apply, as well as being effective in predicting the T a -P relation in climatically different regions (figure 4). The variations in the empirical relation (particularly in dry conditions) are shown to be separated by the statistical significance of the ∆T a -∆P regressions, with the statistically significant regressions consistently showing more negative ∆T a -∆P slopes (figure 3). That pattern indicates that in addition to the primarily thermodynamic processes considered here (i.e. wetness index in this study), the atmospheric dynamics also play an important role in changing T a (Suarez-Gutierrez et al 2020). It should be noted that this study was conducted at ∼100 km spatial scale, we expect the general findings would hold but show slight difference with a change in spatial resolution because of different dynamical and thermodynamical processes being resolved. Future studies are needed to better separate and attribute the contribution of various dynamical and thermodynamical drivers of T a change.
We note that under extremely arid conditions (P/E o → 0) the empirical relation reported here (figure 3) predicts that the mean annual T a would increase by around 0.002 K for a decrease in annual P of 1 mm. Hence for a decrease in annual P of say 100 mm, which would be typical of the inter-annual variations that actually occur in many arid environments, we anticipate inter-annual variations in T a of up to 0.2 K in a single year due to inter-annual variation in P. The magnitude of that variation is important given that the current global warming signals over land have a typical magnitude of 0.2 K per decade (IPCC 2013). This highlights the potential importance of hydro-climatic extremes (e.g. droughts) or long-term trends of P in modifying T a independently of long term climate trends.
It should be noted that the above empirical relation is only applicable in regions that have limited influence of snow/ice cover and irrigation. Further, we focus on the annual time scale and implicitly assume that precipitation (P) is the only source of water. At shorter time scales, e.g. seasonal, we expect that variations in soil moisture and ground water will also play an important role in the T a -P relation, particularly in dry regions (e.g. Berg et al 2015, Schwingshackl et al 2017. We suspect that ignoring changes in storage might also explain some of the scatter in the inter-annual T a -P relation (see figure 3). Therefore, future work that includes the effect of changes in water storage at monthly/seasonal time scales is needed.

Conclusions
In this study, we quantitatively estimate the dependence of near-surface air temperature T a on variations in precipitation P (denoted as dT a /dP) using aridity as a predictor. Observations generally show T a to be negatively correlated with P in dry environments but independent of P in wet environments. We then develop a quantitative (empirical) regression to predict T a -P relation based on aridity (P/E o , with E o defined as the net radiation but expressed as an equivalent depth of water). With this proposed framework, the inter-annual variations in T a due to those in P are estimated using separate piecewise linear functions for dry (P/E o ≤ 1, dT a /dP ∼ 0.0023 * P /E o -0.0023) and wet (P/E o > 1, dT a /dP ∼ 0) environments. This framework is further tested in three independent regions and found to be both practical to apply, and also effective in predicting the regional T a -P relations. This new framework will be useful, especially in dry environments, to quantify variations in air temperature during wet/dry extremes. Future work that includes the effect of changes in water storage at monthly/seasonal time scales is needed.